We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
An important mode of stabilization of cations in biochemical reactions is interaction with the π systems-of aromatic residues. As part of an investigation of the interaction of carbocations with aromatic π systems, a study of various model...
The Border Gateway Protocol (BGP) that manages inter-domain routing on the Internet lacks security. Protective measures using public key cryptography introduce complexities and costs. To support authentication and other security functionality in...
Interaction with aromatic π systems has become recognized as an important mode of stabilization of carbocation intermediates in biological reactions. To gain insight into such carbocation-π interactions, we have undertaken a study of...
Social networks -- Mathematical models. Social networks -- Computer simulation. Dynamics. Social sciences -- Network analysis -- Methodology.
Detecting the significance of relationships between people is a complicated and difficult task. This is especially true when these relationships are intermixed with hundreds of different mundane and ordinary interactions that are simply background...
The novel heptachloro-1'-methyl-1,2'-bipyrrole (""Q1"") ( 1 ) is a natural organohalogen that has been detected in more than 100 worldwide environmental samples. In recent years mixed halogenated 1,2'-bipyrroles have also been detected in several...
Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...